Merge templates with 14C, C, and N data
Radiocarbon analyses for the 2001 samples were not run originally, but were completed on archived samples in 2020.
Fig. 10. Mean profile \(\Delta\)14C for 2001 samples
Caption: Mean \(\Delta\)14C by depth for each site in 2001. Error bars show ±1 standard deviation, solid vertical line shows \(\Delta\)14C of the atmosphere in the year of sampling.
Fig. 10. Profile \(\Delta\)14C for 2009 samples
Caption: Profile \(\Delta\)14C by depth for each site in 2009. Solid vertical line shows \(\Delta\)14C of the atmosphere in the year of sampling. Error bars not shown as only a single replicate profile was analyzed per site.
Fig. 10. Mean profile \(\Delta\)14C for 2019 samples
Caption: Mean \(\Delta\)14C by depth for each site in 2019. Error bars show ±1 standard deviation, solid vertical line shows \(\Delta\)14C of the atmosphere in the year of sampling.
Fig. 10. Mean profile \(\Delta\)14C for 2001 and 2019 samples
Caption: Mean \(\Delta\)14C by depth for each site in 2001 and 2019. Error bars show ±1 standard deviation. Vertical lines show \(\Delta\)14C of the atmosphere in 2001 (solid) and 2019 (dashed).
Fig. 10. Rep 1 \(\Delta\)14C-CO2 of 2019 bulk soil incubations
Caption: \(\Delta\)14CO2 by depth for each site in 2019. (Still waiting for data from laboratory duplicates). Note that the 10-20 cm increment sample from the cold granite site appears to have been contaminated: \(\Delta\)14C-CO2 = -396.7.
Fig. 10. \(\Delta\)14C of 2019 bulk soil incubations and corresponding bulk soil
Caption: \(\Delta\)14C of bulk soil and respired CO2 by depth for each site in 2019. Error bars show one standard deviation for bulk soil, points show mean of three replicate profiles for bulk soils and single observations for respired CO2 (still waiting for data from laboratory duplicates).
Fig. 10. Regression of 2019 bulk soil incubations and corresponding bulk soil \(\Delta\)14C
Caption: Regressions of \(\Delta\)14C of bulk soil and respired CO2 by depth for each site in 2019. Error bars show one standard deviation for bulk soil, points show mean of three replicate profiles for bulk soils and single observations for respired CO2 (still waiting for data from laboratory duplicates).
Fig. 10. Time series of \(\Delta\)14C by depth, as measured
Caption: Points show mean of three profile replicates for 2001 and 2019 samples. Error bars show ± 1 standard deviation of the mean (only a single profile was analyzed in 2009).
Fit splines to 2009 data to predict at 2001 depths
Soils collected in both the 2001 and 2009 sampling campaigns were sampled by horizon, but the depth intervals differed between the two sampling years. In 2009, full profiles were excavated for each site, as opposed to the shorter profiles collected in 2001 from the GR and AN sites. Radiocarbon was measured on all three replicate profiles at each site for the 2001 samples, but only for one of the replicate profiles at each site in 2009, e.g. ANpp rep2, etc.
In order to compare the radiocarbon profiles between 2001, 2009, and 2019 we interpolated both radiocarbon and carbon stock data at 1 cm intervals for each site in the 2009 and 2019 datasets, and then summed the carbon-stock-weighted radiocarbon values for each depth interval sampled in 2001. A monotonic cubic spline fit was used for the carbon stock interpolation (Wendt and Hauser 2013), and a mass-preserving spline was used to fit the radiocarbon data (Bishop, T.F.A., McBratney, A.B., Laslett, G.M., (1999) Modelling soil attribute depth functions with equal-area quadratic smoothing splines. Geoderma, 91(1-2): 27-45).
Fig. 10. Time series of \(\Delta\)14C by depth (2001, 2009, 2019)
Caption: Points for 2001 samples show the mean \(\Delta\)14C values at the measured depths. Points for 2009 and 2019 samples are spline-fitted estimates of \(\Delta\)14C predicted for the same depth intervals as measured in 2001. Error bars show ± 1 standard deviation of the mean of three replicate profiles for 2001 and 2019 samples (only a single profile was analyzed in 2009).
Fig. 10. Time series of \(\Delta\)14C by depth (splined to 2019 depths)
Caption: Points for 2019 samples show the mean \(\Delta\)14C values at the measured depths. Points for 2001 and 2009 samples are spline-fitted estimates of \(\Delta\)14C predicted for the same depth intervals as measured in 2019. Error bars show ± 1 standard deviation of the mean of three replicate profiles for 2001 and 2019 samples (only a single profile was analyzed in 2009). NB: Only two depth intervals were measured at the cool and cold andesite sites (max depth of 27 and 28 cm, respectively), so linear extrapolation (using the slope of the last 1cm spline-fitted depth increment) was used to extend the profiles to 30 cm.
The goal of this modeling exercise is to see how parent material and climate/ecosystem affect estimates of soil carbon ages and transit times. Bulk soil 14C observations from 2001, 2009, and 2019 will be used to constrain the carbon models, as well as observations of 14C-CO2 from laboratory soil incubations of soils collected in 2001 and 2019. Previous work has indicated that the carbon stocks at these sites is likely at equilibrium, so we will apply the steady-state assumption to the modeling.
One pool models have been shown repeatedly to be inadequate for describing soil carbon dynamics. However, as simple models are easier to constrain, we will start with a two-pool parallel and two-series models, as these are the simplest model system beyond the single pool approach.
The two-pool parallel model requires the following parameters: * decomposition constants for each pool (k1, k2) * input partitioning coefficient (\(\gamma\)) * steady-state carbon stocks (C) * inputs (I) * initial values of 14C
The two-pool series model requires the following parameters: * decomposition constants for each pool (k1, k2) * transfer coefficient (\(\alpha\)) * steady-state carbon stocks (C) * inputs (I) * initial values of 14C
Decomposition rates (k) are related to the amount of 14C in a pre-bomb system (fraction modern, F) at steady-state by the following equations (cf. Schuur, Druffle, and Trumbore, 2016): >Eq. 1
\[F = \frac{k}{k + \lambda}\] >Eq. 2
\[k = \frac{\lambda \cdot F}{1 - F}\] >where \(\lambda\) is the radioactive decay constant (1/8267).
As the decomposition rates will vary, the initial 14C content can be determined dynamically with equation 1.
Carbon stocks are known, while inputs will be estimated and are related to the steady-state conditions by the following equation: >Eq. 3
\[I = (k_{1} \cdot C_{1}) + (k_{2} \cdot C_{2})\] >where C1 and C2 are the carbon stocks of the two model pools.
Both stocks and inputs can be scaled to the known value of the total carbon pool once the steady-state parameters (k1, k2, and \(\gamma\) or \(\alpha\)) have been determined. Pool sizes are a function of the inputs and input partitioning coefficient at steady-state.
A Monte-Carlo Markov chain approach will be used for parameter estimation in combination with an initial optimization algorithm to determine the best set of initial parameters.
Initial model fitting was performed for both model structures using generous parameter ranges [0, 1] for all three parameters (k1, k2, \(\gamma\) or \(\alpha\)). The initial parameter set was found by fitting the models by eye, followed by optimization with the function “modFit” (R package FME), using the Nelder-Mead algorithm. The best set of parameters found by modFit was then used as the input to a Monte Carlo Markov Chain (MCMC), using the function “modMCMC” (R package FME). The number of iterations for the MCMC optimization was set at 5000 intially, with delayed rejection employed to increase efficiency.
The sum of the mean squared error for the best parameter set was slightly lower for the parallel structure than for the series structure. Additionally, the overall mean error of the residuals was also lower for the parallel structure, moderately so for the bulk C observations but substantially so for the respiration observations (in andesite and granite soils in particular).
However, these initial fits yielded unrealistic parameter estimates for multiple sites, particularly at the lower depths. Additionally, the modFit output showed very high correlation between the parameters for both model structures (slightly higher for the two-pool series model).
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This section needs some work.